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wu :: forums    riddles    medium (Moderators: Eigenray, william wu, ThudnBlunder, towr, SMQ, Icarus, Grimbal)    STRING OF PRIMES « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: STRING OF PRIMES  (Read 429 times) pcbouhid Uberpuzzler     Gender: Posts: 647 STRING OF PRIMES   « on: Nov 24th, 2005, 10:19am » Quote Modify Starting from an arbitrary prime of 3 digits you choose, construct a sequence of distinct 3-digit primes such that every one is formed by the 2 rightmost digits of the previous one plus any digit juxtaposed to the right - e.g. 113, 137, 373,... What is the maximum number of distinct primes that YOU can achieve in the sequence?   We are not asking for the maximum number of primes that can be achieved, we are asking for YOUR maximum number. IP Logged Don´t follow me, I´m lost too. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: STRING OF PRIMES   « Reply #1 on: Nov 24th, 2005, 10:31am » Quote Modify With or without the computer? Failing that, is a list of primes allowed, or should I do that from memory also? IP Logged Wikipedia, Google, Mathworld, Integer sequence DB pcbouhid Uberpuzzler     Gender: Posts: 647 Re: STRING OF PRIMES   « Reply #2 on: Nov 24th, 2005, 10:44am » Quote Modify towr, you can have at hand a list of primes, but the intention is to see who can achieve more primes without using a computer. IP Logged Don´t follow me, I´m lost too. JocK Uberpuzzler     Gender: Posts: 877 Re: STRING OF PRIMES   Priem03.doc « Reply #3 on: Nov 24th, 2005, 10:56am » Quote Modify on Nov 24th, 2005, 10:44am, pcbouhid wrote: towr, you can have at hand a list of primes, but the intention is to see who can achieve more primes without using a computer.   Ok, let's make sure everyone starts from the same 'pole' position then.. ;)   (see attached list of 3-digit primes)   IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. JocK Uberpuzzler     Gender: Posts: 877 Re: STRING OF PRIMES   « Reply #4 on: Nov 24th, 2005, 11:06am » Quote Modify It is not so difficult actually to get lengthy sequences. My first two trials (by hand) yielded:   113, 131, 311, (113 = repeat)   113, 131, 313, 137, 373, 733, 331, 317, 179, 797, 971, 719, 193, 937, 379, (797 =  repeat)   In most of the cases you have multiple choices for the next prime. IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. JohanC Senior Riddler     Posts: 460 Re: STRING OF PRIMES   « Reply #5 on: Nov 24th, 2005, 11:14am » Quote Modify Following your wording, you would be allowed to use the same prime multiple times. Although they don't count for calculating the maximum, they help to get a longer string. Or did I read something wrong? IP Logged JocK Uberpuzzler     Gender: Posts: 877 Re: STRING OF PRIMES   « Reply #6 on: Nov 24th, 2005, 1:50pm » Quote Modify on Nov 24th, 2005, 11:14am, JohanC wrote: Following your wording, you would be allowed to use the same prime multiple times. Although they don't count for calculating the maximum, they help to get a longer string. Or did I read something wrong?   If that is allowed, I am quite certain that one can get a sequence containing at least all 31 three digit primes that don't contain an even digit or the digit '5'...   « Last Edit: Nov 24th, 2005, 1:52pm by JocK » IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: STRING OF PRIMES   « Reply #7 on: Nov 24th, 2005, 1:51pm » Quote Modify I don't feel like going further than   521 211 113 131 313 137 373 739 397 977 773 733 331 317 179 797 971 719 191 919 193 937 379   at the moment. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB pcbouhid Uberpuzzler     Gender: Posts: 647 Re: STRING OF PRIMES   « Reply #8 on: Nov 25th, 2005, 6:11am » Quote Modify JohanC and jock, the problem states tacitly "construct a sequence of distinct 3-digit primes" .   And towr, there´s at least one "longer" string than yours, with 26 primes. « Last Edit: Nov 25th, 2005, 6:12am by pcbouhid » IP Logged Don´t follow me, I´m lost too. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: STRING OF PRIMES   « Reply #9 on: Nov 26th, 2005, 1:38pm » Quote Modify Oh, I knew there were longer ones (well, strongly suspected as much at least). I just got tired of processing the list of primes by hand. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB pcbouhid Uberpuzzler     Gender: Posts: 647 Re: STRING OF PRIMES   « Reply #10 on: Nov 27th, 2005, 4:28am » Quote Modify I understand. For this kind of puzzle, it´s better using a computer but, in a contest, to make it fair with the others, it´s not allowed. And this is not a contest.   A computer program found 1820 sequences of 26 primes, and 2 of them are:   241, 419, 191, 919, 193, 937, 373, 733, 331, 317, 179, 797, 977, 773, 739, 397, 971, 719, 199, 991, 911, 113, 131, 313, 137, 379.   And:   941, 419, 199, 991, 919, 193, 937, 379, 797, 977, 773, 739, 397, 971, 719, 191, 911, 113, 131, 313, 137, 373, 733, 331, 317, 179. IP Logged Don´t follow me, I´m lost too. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: STRING OF PRIMES   « Reply #11 on: Nov 27th, 2005, 7:30am » Quote Modify So is that the maximum then? Or wasn't it a complete search?   I had thought about drawing a graph of all candidate numbers and trying to find the longest path to visit each vertex at most once.   Which is also something a computerprogram might use.   Of course the first step is to seperate the primes of which the first two digits form an even number from those where it's odd. You can't use the first group anywhere except at the start. And you can throw out the few with a middle 0 completely. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB pcbouhid Uberpuzzler     Gender: Posts: 647 Re: STRING OF PRIMES   « Reply #12 on: Nov 27th, 2005, 12:34pm » Quote Modify The computer program is not mine, but its result match the result found in another source (26 primes). IP Logged Don´t follow me, I´m lost too. herbs Guest Re: STRING OF PRIMES   « Reply #13 on: Nov 28th, 2005, 7:38pm » Quote Modify Remove None exist. The primes of Hebrew function H(x,Y,z)**2 over (a->x) make ( 137 373 739 397 977 773 733 331 317 179 797 971 719 191 919 193 937 379) invalid. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: STRING OF PRIMES   « Reply #14 on: Nov 29th, 2005, 1:12am » Quote Modify on Nov 28th, 2005, 7:38pm, herbs wrote: None exist. The primes of Hebrew function H(x,Y,z)**2 over (a->x) make ( 137 373 739 397 977 773 733 331 317 179 797 971 719 191 919 193 937 379) invalid. Ah, now things are making sense. You're just making things up and posting it under different names..  Naughty little troll IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Barukh Uberpuzzler     Gender: Posts: 2276 Re: STRING OF PRIMES   « Reply #15 on: Nov 29th, 2005, 2:28am » Quote Modify towr, could you please explain herb's cryptic message, so that it will make sense for other members as well?     IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: STRING OF PRIMES   « Reply #16 on: Nov 29th, 2005, 2:55am » Quote Modify on Nov 29th, 2005, 2:28am, Barukh wrote: towr, could you please explain herb's cryptic message, so that it will make sense for other members as well? It's sort of like technobabble; at first glance it sounds good but in actuallity it means nothing. I think he's the same person that posted in (at least) two other threads. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB pcbouhid Uberpuzzler     Gender: Posts: 647 Re: STRING OF PRIMES   « Reply #17 on: Nov 29th, 2005, 6:26am » Quote Modify See his comment in  "A SYSTEM OF MODULAR EQUATIONS". « Last Edit: Nov 29th, 2005, 6:29am by pcbouhid » IP Logged Don´t follow me, I´m lost too. Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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